Abstract
A unidirectional stationary binary mixture motion in a horizontal channel is under study. New exact solution of the Oberbeck–Boussinesque equations is constructed for description of the mentioned flow. The obtained solution is applied for investigation of the separation process in mixture of water and isopropanol located between two differently heated rigid walls
Highlights
Governing equationsUθx = χ(θxx + θyy), ucx = D(cxx + cyy) + Dθ(θxx + θyy), where u = u(y) is the horizontal velocity, θ = θ(x, y) is the temperature, c = c(x, y) is the light component concentration, g = (0, −g, 0) is the gravity acceleration vector, p∗ = p − gρ0y is the modified pressure
Received 02.04.2019, received in revised form 03.06.2019, accepted 20.08.2019 A unidirectional stationary binary mixture motion in a horizontal channel is under study
It is devoted to exhausted description of constructing exact solution of the Oberbeck–Boussinesque equations for unidirectional motions in case of quadratic dependence of temperature and concentration with respect to horizontal coordinate
Summary
Uθx = χ(θxx + θyy), ucx = D(cxx + cyy) + Dθ(θxx + θyy), where u = u(y) is the horizontal velocity, θ = θ(x, y) is the temperature, c = c(x, y) is the light component concentration, g = (0, −g, 0) is the gravity acceleration vector, p∗ = p − gρ0y is the modified pressure. We deal with normal thermal diffusion at Dθ < 0 when the light component tends to more heated region. If Dθ > 0 the light component tends to less heated region Equations (1) describe the binary liquid motion in the Oberbeck–Boussinesq approximation It means that the equation of state has the form ρ = ρ0(1 − β1θ − β2c), where β1, β2 are the thermal and concentration extension coefficients, ρ0 is the average mixture density.
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